Homework_07
Shelby N. Scarfo
2024-02-28
I am using a bottom trawling dataset that looks at the catch per unit effort (CPUE) of alewife throughout the three different portions (north, central, south) of the main lake in Lake Champlain. I am not expecting to see any significant differences in CPUE between these regions because they are all part of the main lake and are not geographically isolated from eachother.
Running ANOVA and Tukey tests on my own data
#Loading in data and getting attributes
ALW_CPUE_basin <- read.csv("ALW_CPUE_basin.csv")
ALW_CPUE_basin$minor_basin <- factor(ALW_CPUE_basin$minor_basin, levels = c("North Main Lake", "Central Main Lake", "South Main Lake"))
str(ALW_CPUE_basin)## 'data.frame': 345 obs. of 3 variables:
## $ sampleID : chr "BOT_04132018_01" "BOT_04132018_02" "BOT_04132018_03" "BOT_04132018_04" ...
## $ minor_basin: Factor w/ 3 levels "North Main Lake",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ CPUE : num 8.528 37.5 68.903 255.989 0.667 ...## sampleID minor_basin CPUE
## Length:345 North Main Lake : 72 Min. : 0.500
## Class :character Central Main Lake:218 1st Qu.: 4.003
## Mode :character South Main Lake : 55 Median : 20.020
## Mean : 86.624
## 3rd Qu.: 90.337
## Max. :1404.000ALW_CPUE <- group_by(ALW_CPUE_basin, minor_basin) %>%
summarise(
count = n(),
mean = mean(CPUE, na.rm = TRUE),
sd = sd(CPUE, na.rm = TRUE)
)
print(ALW_CPUE) # This shows the sample sizes, means, and variances for each group## # A tibble: 3 × 4
## minor_basin count mean sd
## <fct> <int> <dbl> <dbl>
## 1 North Main Lake 72 100. 200.
## 2 Central Main Lake 218 90.1 170.
## 3 South Main Lake 55 55.0 119.#Running ANOVA on data and creating figure
res.aov <- aov(CPUE~minor_basin, data = ALW_CPUE_basin)
summary(res.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## minor_basin 2 71360 35680 1.239 0.291
## Residuals 342 9851925 28807## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = CPUE ~ minor_basin, data = ALW_CPUE_basin)
##
## $minor_basin
## diff lwr upr p adj
## Central Main Lake-North Main Lake -10.27977 -64.58625 44.02672 0.8963867
## South Main Lake-North Main Lake -45.40800 -116.95666 26.14065 0.2950901
## South Main Lake-Central Main Lake -35.12824 -95.41458 25.15810 0.3569643ANOplot <- ggplot(data = ALW_CPUE_basin)+
aes(x= minor_basin, y = CPUE, fill = minor_basin) +
geom_boxplot()
ANOplot
The ANOVA and tukey tests shows that there is no statistical difference (p > 0.05) between CPUE in the three regions of the main lake.
Making fake dataset that has the same attributes as my real one
# Giving this data the same parameters as my original data
nGroup <- 3
nName <- c("North Main Lake", "Central Main Lake", "South Main Lake")
nSize <- c(72, 218, 55)
nMean <- c(100.4, 90.1, 54.9)
nSD <- c(199.7, 169.8, 119.2)
ID <- 1:(sum(nSize))
#Used rtruncnorm to set my bottom limit to 0 because I can't have a negative catch
modelCPUE <- c(rtruncnorm(n=nSize[1], a = 0, b = Inf, mean=nMean[1],sd=nSD[1]),
rtruncnorm(n=nSize[2], a = 0, b = Inf, mean=nMean[2],sd=nSD[2]),
rtruncnorm(n=nSize[3], a = 0, b = Inf, mean=nMean[3],sd=nSD[3]))
TGroup <- rep(nName,nSize)
ANOdata <- data.frame(ID,TGroup,modelCPUE)
ANOdata$TGroup <- factor(ANOdata$TGroup, levels = c("North Main Lake", "Central Main Lake", "South Main Lake"))
str(ANOdata)## 'data.frame': 345 obs. of 3 variables:
## $ ID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ TGroup : Factor w/ 3 levels "North Main Lake",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ modelCPUE: num 314.3 349.8 146.9 46.2 185.3 ...## Df Sum Sq Mean Sq F value Pr(>F)
## TGroup 2 267462 133731 9.671 8.21e-05 ***
## Residuals 342 4728952 13827
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TestANOPlot <- ggplot(data=ANOdata,aes(x=TGroup,y=modelCPUE,fill=TGroup)) +
geom_boxplot()
print(TestANOPlot)
TukeyHSD(ANOmodel) #This shows that there is no statistic difference between Central Main Lake CPUE and North Main Lake CPUE but there is a statistical difference between the South Main Lake CPUE and the other two regions.## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = modelCPUE ~ TGroup, data = ANOdata)
##
## $TGroup
## diff lwr upr p adj
## Central Main Lake-North Main Lake -45.47622 -83.10096 -7.851469 0.0130323
## South Main Lake-North Main Lake -92.18646 -141.75697 -42.615954 0.0000474
## South Main Lake-Central Main Lake -46.71024 -88.47797 -4.942519 0.0240024Altering the metrics of the fake data to see how the parameters affect statistical significance
#Double the mean of the South Main Lake fake data
set.seed(100)
nGroup <- 3
nName <- c("North Main Lake", "Central Main Lake", "South Main Lake")
nSize <- c(72, 218, 55)
nMean2 <- c(100.4, 90.1, 109.8)
nSD <- c(199.7, 169.8, 119.2)
ID <- 1:(sum(nSize))
meanDubCPUE <- c(rtruncnorm(n=nSize[1], a = 0, b = Inf, mean=nMean2[1],sd=nSD[1]),
rtruncnorm(n=nSize[2], a = 0, b = Inf, mean=nMean2[2],sd=nSD[2]),
rtruncnorm(n=nSize[3], a = 0, b = Inf, mean=nMean2[3],sd=nSD[3]))
TGroup <- rep(nName,nSize)
ANOMeanDubdata <- data.frame(ID,TGroup,meanDubCPUE)
ANOMeanDubdata$TGroup <- factor(ANOMeanDubdata$TGroup, levels = c("North Main Lake", "Central Main Lake", "South Main Lake"))
#Run ANOVA and Tukey on doubled South Main Lake mean data
ANOMeanDubmodel <- aov(meanDubCPUE~TGroup,data=ANOMeanDubdata)
summary(ANOMeanDubmodel)## Df Sum Sq Mean Sq F value Pr(>F)
## TGroup 2 82514 41257 2.795 0.0625 .
## Residuals 342 5047412 14759
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANOMeanDubPlot <- ggplot(data=ANOMeanDubdata,aes(x=TGroup,y=meanDubCPUE,fill=TGroup)) +
geom_boxplot()
print(ANOMeanDubPlot)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = meanDubCPUE ~ TGroup, data = ANOMeanDubdata)
##
## $TGroup
## diff lwr upr p adj
## Central Main Lake-North Main Lake -37.633399 -76.50438 1.237585 0.0601281
## South Main Lake-North Main Lake -39.548020 -90.76044 11.664400 0.1652668
## South Main Lake-Central Main Lake -1.914621 -45.06581 41.236567 0.9940039In order for there to be no statistical difference between the North Main Lake and the South Main Lake CPUEs I had to double the original mean of the South Main Lake.
#Change the sample sizes
set.seed(110)
nGroup <- 3
nName <- c("North Main Lake", "Central Main Lake", "South Main Lake")
nSize2 <- c(72, 218, 15)
nMean <- c(100.4, 90.1, 54.9)
nSD <- c(199.7, 169.8, 119.2)
ID <- 1:(sum(nSize2))
sizeCPUE <- c(rtruncnorm(n=nSize2[1], a = 0, b = Inf, mean=nMean[1],sd=nSD[1]),
rtruncnorm(n=nSize2[2], a = 0, b = Inf, mean=nMean[2],sd=nSD[2]),
rtruncnorm(n=nSize2[3], a = 0, b = Inf, mean=nMean[3],sd=nSD[3]))
TGroup <- rep(nName,nSize2)
ANOSizedata <- data.frame(ID,TGroup,sizeCPUE)
ANOSizedata$TGroup <- factor(ANOSizedata$TGroup, levels = c("North Main Lake", "Central Main Lake", "South Main Lake"))
#Run ANOVA and Tukey on altered sample size data
ANOSizemodel <- aov(sizeCPUE~TGroup,data=ANOSizedata)
summary(ANOSizemodel)## Df Sum Sq Mean Sq F value Pr(>F)
## TGroup 2 144287 72144 5.492 0.00454 **
## Residuals 302 3967165 13136
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ANOSizePlot <- ggplot(data=ANOSizedata,aes(x=TGroup,y=sizeCPUE,fill=TGroup)) +
geom_boxplot()
print(ANOSizePlot)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = sizeCPUE ~ TGroup, data = ANOSizedata)
##
## $TGroup
## diff lwr upr p adj
## Central Main Lake-North Main Lake -31.95289 -68.64668 4.7408994 0.1020220
## South Main Lake-North Main Lake -103.02700 -179.64588 -26.4081134 0.0048182
## South Main Lake-Central Main Lake -71.07411 -143.13376 0.9855457 0.0541551In order for there to be no statistical difference between the Central Main Lake and the South Main Lake CPUEs (largest sample size difference) I had to reduce the South Main Lake sample size by 40 to 15.